Analysis of Single$-$Model Assembly Lines

A product whose work content time $=53\mathrm{.}0$ min is to be assembled on a manual production line. The required production rate is $33$ units$/$hr$.$ From previous experience, it is estimated that proportion uptime $=0\mathrm{.}95,$ balance efficiency $=93\%,$ and repositioning time $=6$ sec$.$ Determine $($a$)$ cycle time, $($b$)$ the ideal minimum number of workers required on the line, and $($c$)$ a more realistic estimate of the number of workers on the line when balance efficiency and repositioning time are accounted for.

$($a$)$ The cycle time is

$1\mathrm{.}73$

minute$($s$).$ Submit your answer using THREE decimal places. Example: $2\mathrm{.}123$

$($b$)$ The ideal minimum number of workers required on the line is

$31$

workers. Round your answer.

$($c$)$ Provide a more realistic estimate of the number of workers on the line when balance efficiency and repositioning time are accounted for is

workers. Round your answer.